Particle system not linking particles at the object origin
Okay it looks like the main problem is actually pretty simple. The particle system is set to render from the collection FlowerBunch1, but it looks like Bunch1 is the collection you've been working on. So changing that fixed the worst of the problem. (You can also check Pick Random so it randomly selects a blossom in the collection instead of cycling sequentially)


As an aside, the collections listed with an F (including FlowerBunch1) have a fake user (see also: term in 2.79 manual) keeping them in the blend file, even though they aren't in the scene anymore. If you want to remove these entirely (and you're sure they aren't needed or referenced elsewhere), you can switch the outliner to show the blend file, then right click the collection to delete it from the file.

Or alternatively the fake user can be set/removed in the ID Data sub-menu and the collection added back in with Link to Scene.

At this point the blossoms should be mostly connected correctly. Just make sure to check that all the objects in the collection have their origin where you want it to connect to the branch. The bent blossom Circle.006 is a touch off, and the large bunch object Circle.004 is a little disconnected. It may need to be modified to have the stems come together closer to its origin, so they all appear connected to the branch.


And this goes a bit beyond the scope of your question, but the rotation of the blossoms is also making it hard to tell sometimes where it's connecting. Here's a couple suggestions as a starting point, but do whatever will get the results you're looking for:

Rotating the blossoms to be aligned with the X axis allows the particle system to know which way the blossom is facing

Orienting the particles to the branch's normal so it points outward. Using a bit less random rotation, but with more random phase (spin).


Note: To keep it simple, I removed the bunch (and the empty) from the collection Bunch1 for these examples, so that only the single blossoms would be added to the tree.